If my aim is to carve out a career track of a quant developer or front desk quant, may I know which areas of financial mathematics should I aim to focus and specialise in? For research or when doing a PhD topic for example.

I may be considering to apply and get admitted into the MSc Financial Mathematics at Kings, and then probably go on and complete their PhD in Financial Mathematics as well. But so far, it seems like LSE and Warwick are ahead of Kings in terms of their MSc FinMath, so will doing a MSc FinMath by Kings help to get me a quant or junior quant role? and whats your opinion on KCL's MSc FM at present? On the other hand, should I focus on completing my PhD in FM before seeking out a quant career? and for a PhD in FM, whats your opinion on the one by Kings? Or are others better?

Thanks so much for the sound advice. By the way, will topics on numerical analysis/probability/monte carlo simulation be useful for a quant as well? Its best not to focus on a rather financial topic as compared to a mathematical one am I right?